Pertanyaan

Tentukan limit berikut: x → ∞ lim 3 x 2 − 4 x + 1 2

Tentukan limit berikut:

$x \to \infty lim \frac{2}{3 x ^{2} - 4 x + 1}$

N. Puspita

Master Teacher

Jawaban terverifikasi

Jawaban

nilai limit tersebut adalah 0.

Pembahasan

Pertamalakukan pembagian setiap suku dengan variabel pangkat tertinggi, kemudian substitusi, maka didapat: ingat bahwa sehingga Jadi, nilai limit tersebut adalah 0.

Pertama lakukan pembagian setiap suku dengan variabel pangkat tertinggi, kemudian substitusi, maka didapat:

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator 2 over denominator 3 x squared minus 4 x plus 1 end fraction end cell equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 2 over x squared end style over denominator begin display style fraction numerator 3 x squared over denominator x squared end fraction end style minus begin display style fraction numerator 4 x over denominator x squared end fraction end style plus begin display style 1 over x squared end style end fraction end cell row blank equals cell limit as x rightwards arrow infinity of fraction numerator begin display style 2 over x squared end style over denominator begin display style 3 minus 4 over x plus 1 over x squared end style end fraction end cell row blank blank blank end table$

ingat bahwa limit as x rightwards arrow infinity of a over x to the power of n equals 0 sehingga

$table attributes columnalign right center left columnspacing 0px end attributes row cell limit as x rightwards arrow infinity of fraction numerator begin display style 2 over x squared end style over denominator begin display style 3 minus 4 over x plus 1 over x squared end style end fraction end cell equals cell fraction numerator 0 over denominator 3 minus 0 plus 0 end fraction end cell row blank equals cell 0 over 3 end cell row blank equals 0 end table$

Jadi, nilai limit tersebut adalah 0.